If the total enrgy fo an electron in a hydrogen linke atom in an ecited state is ` - 3. 4 eV` , the the de-Broglie wavelngth of the electron is :

Options

A. `6.6xx10^(-10)`
B. ` 3 xx 10^(10)`
C. ` 5 xx 10^(-9) `
D. ` 9. 3 xx 10 ^(10)`

Answer

A

Explanation

Total energy ` = (-e^2)/(2r_n) =- 3 . 4 eV = E_(1) /n^2`
`:. N^(2) = ( -13 . 6)/( -3 . 4) = 4 :. N=2`
The velovity in II orbit
` = u_(1)/2 = ( 2 . 18 xx 10^8 )/2 cm sec ^(-1)`.
` therefore lambda = h/( mu) = (6.6 xx 10^(27)xx 2)/( 9. 108 xx 10^(-23) xx 2 . 18 xx 10^8)`.
` = 6.6. xx 10^(-10) `
` E_(1) =- 13 . 6 eV`.